ok it's not a 1:1 correlation, but I'm sure there's some kind of relationship. there's an intrinsic conflict of interest - the more you make the app convenient to the point the user doesn't need to interact with it as much, the more you hurt your ad revenue.
(that said, I'm sure a dip in revenue from gmail isn't going to end google)
See, this feature is something that makes GMail very attractive, which results in a high user influx and loyalty. More users, more views.
Additionally the web interface of the GMail is made so well, that I for instance stopped using my IMAP synced local eMail client, effectively watching their ads more (not really, I'm ad resistant, but I'm exposed).
By the way, you want an interesting example? Think of the "I'm feeling lucky" button - a search option on their frontpage which completely bypasses any ads. How much lost revenue has Google experienced because of that one small button? Yet they still keep it.